The initial and final temperatures of liquid in a container are observed to be `7.63 +- 0.4^(@) C and 67.7 +- 0.3 ^(@) C`. Determine the fall in the temperature of the liquid.

Explanation

To determine the fall in temperature of the liquid, we will follow these steps:

### Step 1: Identify the Initial and Final Temperatures
- The initial temperature \( T_i \) is given as \( 7.63 \pm 0.4^\circ C \).
- The final temperature \( T_f \) is given as \( 67.7 \pm 0.3^\circ C \).

### Step 2: Calculate the Fall in Temperature
The fall in temperature \( \Delta T \) can be calculated using the formula:
\[ \Delta T = T_f - T_i \]
Substituting the values:
\[ \Delta T = 67.7 - 7.63 \]
Calculating this gives:
\[ \Delta T = 60.07^\circ C \]

### Step 3: Calculate the Uncertainty in the Fall in Temperature
The uncertainty in the fall in temperature is the sum of the uncertainties in the initial and final temperatures:
\[ \text{Uncertainty} = \text{Uncertainty in } T_f + \text{Uncertainty in } T_i \]
Substituting the values:
\[ \text{Uncertainty} = 0.3 + 0.4 = 0.7^\circ C \]

### Step 4: Present the Final Result
The fall in temperature along with its uncertainty can be expressed as:
\[ \Delta T = 60.07 \pm 0.7^\circ C \]

### Final Answer
The fall in temperature of the liquid is:
\[ 60.07 \pm 0.7^\circ C \]

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